On the theory of the formation of lopsided structure in disk-shaped self-gravitating systems

Many disk galaxies exhibit a lopsided nature, with their nuclei clearly displaced from their geometric centers. This phenomenon is associated with gravitational instability during the early stages of the evolution of these objects. Based on this, the present work investigates the gravitational instability of lopsided perturbation modes in the context of a non-stationary disk model with an anisotropic velocity diagram. Corresponding non-stationary analogues of the dispersion equations for these perturbation modes have been derived. The results of the study are presented as critical dependencies of the initial virial ratio on the disk rotation parameter for different values of the superposition parameter. Based on the analysis of the obtained results, it is established that, within the framework of a non-stationary disk model, lopsided perturbation modes exhibit various types of instability depending on the values of the parameters of the non- stationary model of disk-shaped self-gravitating systems.